Piezoelectric resonator with grid-like electrodes

ABSTRACT

A piezoelectric resonator (100) with an attenuated spurious response. The resonator (100) includes a piezoelectric crystal plate (102) having opposite surfaces (104, 106), electrodeS (108, 114) positioned in overlying relationship on each of the opposite surfaces (104, 106), the electrodes (108, 114) being substantially coextensive and opposite, and providing a primary frequency mode of operation and spurious modes upon suitable energization, and the electrodes (108, 114) having a grid-like structure (124) to provide a substantially uniform distribution of electrical charges over an electroded region (126).

FIELD OF THE INVENTION

This invention relates generally to frequency control devices and, inparticular, to a piezoelectric resonator with grid-like electrodes.

BACKGROUND OF THE INVENTION

One of the problems encountered with piezoelectric resonators are theunwanted spurious responses, clustered around the fundamental andovertone responses.

The exact level of spurious (unwanted) responses is difficult to predictin advance, before the physical piezoelectric device is actually built.However, the general relationship of the spur response level todifferent device parameters is well known. The theory relating thepiezoelectric device physical properties to the presence and level ofspurious responses, is known as the Energy Trapping Theory. According tothe theory, one of the parameters strongly affecting the existence ofspurious responses, is so-called "mass loading". In a simple case, thisparameter can be related to the actual mass of the metal electrode ofthe piezoelectric device. More precisely, the factor of primaryimportance is the difference between the mass per unit area of theelectroded region and the mass per unit area of the unelectroded regionof the device. In many commercial devices, this parameter is controlledby the choice of electrode metal and the thickness of the electrode.

Controlling the spurious responses becomes even more critical withovertone devices. The existence of spurious responses in overtonedevices can be minimized when lightweight metal, such as aluminum, isused and the electrode thickness is kept to a minimum, but which isstill sufficient to maintain electrical conductivity.

This invention relates to reducing the mass loading effect through anapproach different from simply reducing the electrode mass of a solidelectrode.

There exists a need for an improved arrangement for fabricatingpiezoelectric resonators, such as quartz crystal blanks, in whichunwanted spurious responses can be minimized.

A structure which helps minimize unwanted spurs in fundamental andovertone responses, would be considered an improvement in the art.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified perspective view of a circular crystal blank withmass loading structures surrounding the electrodes (or tiles), some ofthe tiles on the bottom are shown in phantom, in accordance with thepresent invention.

FIG. 2 is an alternate embodiment, including a top view of a rectangularcrystal blank, showing a plurality of mass loading structures (tiles)surrounding the electrodes, the bottom view being a mirror image of thetop view with the exception of the ground electrode tabs being different(in phantom), in accordance with the present invention.

FIG. 3 is a frequency response of a crystal blank without the massloading structures of the present invention.

FIG. 4 is a frequency response of the crystal blank shown in FIG. 1 inaccordance with the present invention.

FIG. 5 is a top view of a rectangular piezoelectric resonator withgrid-like electrodes, in accordance with the present invention.

FIG. 6 is a bottom view, of the piezoelectric resonator of FIG. 5, inaccordance with the present invention.

FIG. 7 is a frequency response of the piezoelectric resonator shown inFIGS. 5 and 6, in accordance with the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

In FIG. 1, a piezoelectric resonator with an attenuated spuriousresponse is shown, in accordance with the present invention. In itssimplest form, the resonator 10, includes a piezoelectric crystal plate12 having opposite top and bottom surfaces 14 and 16; top and bottomelectrodes 18 and 24 positioned in overlying relationship on each of thefirst and second (top and bottom) surfaces 14 and 16, the electrodes 18and 24 being substantially coextensive and opposite, and providing aprimary frequency mode of operation and spurious modes upon suitableenergization; and a plurality of mass loading structures 34 on at leastone of the surfaces substantially surrounding at least one of theelectrodes 18 and 24. Preferably, the top and bottom electrodes 18 and24 each includes a tab 30 and 32, for suitable electrical connection toa power source.

This structure addresses reducing the mass loading effect through anapproach different from simply reducing the electrode mass. Asubstantially uniform pattern of masses (or structures) can be depositedin proximity to the electrode 18. These structures increase the massloading in the non-electroded region of the piezoelectric device.Because of this, the difference in mass loading between the electrodedregion and the non-electroded region is minimized. This can result inreducing the level of spur responses, as illustrated in FIG. 4.

Although there are distinct advantages to using precious metals forelectrode material, their use is almost exclusively restricted tofundamental mode devices. This is because common precious metals, suchas gold and metal, are heavy and would mass load an overtone deviceexcessively, which in turn would produce high levels of spur responses.This invention provides for improved manufacturing flexibility, byallowing the use of heavy metals as an electrode material for overtonedevices (as well as light metals), if desired.

In more detail, the plurality of mass loading structures 34 includefirst (top) structures 36 on first (top) surface 14 and second (bottom)structures 38 on second surface 16, with piezo spacings 40 betweenadjacent structures 34 and piezo spacings 42 between these structures 36and 38 and the electrodes 18 and 24. These spacings 40 and 42 comprisethe piezoelectric material itself. The region in proximity to theelectrodes 18 and 24 can be defined as an electroded region 44 and theregion surrounding the electrodes can be referred to as a surroundingregion 46. The spacings 40 and 42 are substantially similar to minimizethe mass loading effect and are non-conductive so that the mass loadingstructures 34 are insulated from and not electrically connected to theelectrodes.

The resonator 10 in FIGS. 1 and 2, is particularly adapted forminimizing spurious modes of oscillation for overtone crystals andfilters. With the minimizing of mass loading between the electrodedregion 44 and non-electroded region 46 in overtone devices, heavy orlightweight metals can be used, which can simplify and facilitate massproduction of such devices in certain circumstances. For example, acompany that only has the ability to plate heavy metals on a crystal cannow manufacture overtone oscillators.

In one embodiment, the plurality of mass loading structures 34 include asubstantially repeating and uniform pattern in proximity to theelectrode 18 (and 24). In a preferred embodiment, the mass loadingstructures 34 include first and second structures 36 and 38 located onboth surfaces 14 and 16, and include substantially identical repeatingpatterns (or mirror images), for improved attenuation of spuriousresponses. According to the Energy Trapping Theory, the factor thatcontrols the spur responses is the difference in mass loading betweenthe electroded region 44 and the non-electroded region 46. Normally, thedifference is equal to the mass loading of the electrode material,because the area surrounding the electrode is not subject to massloading. By using the substantially repeating pattern of the massloading structures 34, the effect of the electrode mass loading can beminimized, because the non-electroded region 46 is purposely populatedwith masses or structures 34. The difference in mass loading between theelectroded region 44 (defined as the area between left and rightsections 20 and 22 of the top electrode 18 and left and right sections26 and 28 of bottom electrode 24) and non-electroded region 46 cantherefore be decreased, with improved results, as shown for example inFIG. 4.

The geometric shapes of the structures 34 can vary widely. For example,they can include but are not limited to rectangles, squares, circles,polygons, octagons, sextagons, and the like. The shapes of structures 34can vary widely because they do not function as individual electrodes.They collectively perform a mass loading function in the non-electrodedregion 46. In the embodiment shown in FIGS. 1 and 2, the structures 34are generally rectangles or squares, for maximizing the density of thesestructures in the non-electroded region 46 immediately in proximity tothe electrode 18 (and 24). As should be understood by those skilled inthe art, other geometric shapes can be used, and are considered withinthe scope of this invention.

The resonator 10 can include at least one of the surfaces 14 and 16having a high density of structures 34 positioned substantiallyimmediately in proximity to at least one of the electrodes 18 and 24. Ina preferred embodiment, the mass loading structures 36 and 38 arepositioned immediately in proximity to the electrodes 18 and 24 on bothsurfaces 14 and 16, in the surrounding (non-electroded) region 46. In apreferred embodiment, the (tiles) structures 36 and 38 include an areaat least as large as the areas of the electrodes 18 and 24, andpreferable are larger and are placed immediately adjacent to theelectrodes 18 and 24, for an improved reduction of spurs. The top andbottom structures 36 and 38 collectively approach the weight per unitarea of the weight per unit area of the electrodes 18 and 24, tominimize the difference in the mass loading between the electrodedregion 44 and non-electroded region 46.

Also in a preferred embodiment, the thickness of the structures 36 and38 are substantially equal to the thickness of the top and bottomelectrodes 18 and 24, for ease of manufacturing and improved attenuationof spurious responses.

The gaps, defined by spacings 40 and 42 between the various structures,should normally be kept small, so as to allow the structures 34 to covera significant area of the non-electroded region 46, for improvedresponses. In a preferred embodiment, the structures 36 and 38 cover atleast 50% or more of the non-electroded region 46, for improvedresponses.

As illustrated in FIG. 1, each of the structures 34 has an area smallerthan one of the electrodes 18 and 24, because they function as massloading devices. If the structures 34 were larger than the electrodes,they could exhibit their own resonant effects, which may not beparticularly desirable in this application.

The thicknesses of the first and second mass loading structures 36 and38 and the electrodes 18 and 24 can be substantially similar. In oneembodiment, they are both made out of a conductive material. In apreferred embodiment, the material is a metal such as aluminum (lightmetal), or gold or silver (heavy metals) for using conventionalapplication techniques to the crystal 12.

The electrodes must be made of a conductive material so there is flow ofelectrical charges to and from the device, whereas the structures 34 canbe made of a conductive or non-conductive material. There aresubstantially no restrictions on the electrical properties of thematerial of structures 34, because they do not perform any significantelectrical function. However, the material used for structures 34 shouldbe sufficiently stable to minimize the introduction of any significantshifts to the device frequency. For mass production purposes, thestructure 34 and electrodes 18 and 24 are made conductive and can besuitably plated or masked in one step.

The electroded region 44 includes a natural resonance frequency and thenon-electroded region 46 includes another natural resonance frequency,having a substantially small predetermined difference, because of theminimal difference in mass between the electroded region 44 andnon-electroded region 46. More particularly, the electroded region 44has a natural frequency which is determined primarily by the mass of theelectrode material and the thickness of the quartz blank in that region.The non-electroded region 46 has a natural frequency determinedprimarily by the mass of the material of structures 34 and the thicknessof the quartz blank in the non-electroded region. The existence of themass structures 34 reduces the difference in frequency between these tworegions. As this difference becomes smaller fewer undesired spuriousresponses can be trapped in the electroded region thereby improving thespurious response characteristics of the device.

A more detailed explanation follows. Any resonant structure such as ablank with electrodes has a series of natural resonant frequencies whichare determined by the nature of the material, the dimensions of thematerial and any constraints placed on the acoustic system such as theaddition of mass to the surface. The combination of the basic materialand the dimensions of the material gives rise to it's natural frequency.AT crystals are made by selecting a particular orientation with respectto the crystallographic axes in quartz and then are fabricated into athin disk. This shaping enhances the "thickness shear" mode of vibrationwhich is the desired mode of vibration.

Unfortunately, there are a series of vibrations which are also thicknessshear types of vibration and are related to the desired thickness shear.Fortunately they are always slightly higher in frequency than thedesired mode but they do cause some problems such as spurious responsesin filter crystals.

The weakness or strength of a response is related to the "Q" orresistance of that mode of vibration. A high "Q" or good response meansvery little of the energy which drives the vibration is lost (i.e., theresistance of that mode is low).

A vibration can only travel through the material if it's frequency ishigher than the natural frequency of the material. The desired mode'sfrequency is exactly equal to the natural frequency of the electrodedarea. The area outside of the electrode is higher. This causes thedesired mode to be "trapped" under the electrode. If a mode has afrequency higher than the unelectroded region it will be able to travelbeyond the electroded region towards the edges of the crystal blank.

"Trapped" vibrations have a very high Q because there is little loss ofenergy outside of the electroded region. "Untrapped" vibrations(frequencies higher than the non-electroded region) can travel beyondthe electrode region and therefore can lose energy to other structuressuch as the edge of the blank or the mounting structure. This causesthem to have a low "Q" or weak responses.

Therefore there is a range of frequencies between the frequency of theelectroded region and the frequency of the non-electroded region wherespurs can become trapped causing them to have a high Q and a strongresponse. Adding mass outside the electrode causes the frequency of thenon-electroded region to get closer to the frequency of the electrodedregion thereby narrowing the range of frequencies where spurs can betrapped. This is the reason the added mass outside the electrode works.It allows the spurious frequencies to escape the electroded region anddissipate energy. This reduces their "Q" (increases their resistance)and makes their response very weak, thus minimizing spurious responses.

In a preferred embodiment, the piezoelectric resonator 10 includes apiezoelectric crystal plate 12 having opposite surfaces defined as afirst surface 14 and a second surface 16; electrodes 18 and 24 arepositioned in overlying relationship on each of the surfaces 14 and 16,the electrodes 18 and 24 are substantially coextensive and opposite, andprovide a primary frequency mode of operation and spurious modes uponsuitable energization; and a plurality of mass loading structures 34 onfirst and second surfaces 14 and 16 substantially surrounding theelectrodes 18 and 24. This structure helps to minimize spuriousresponses and is adapted to improving mass production of resonators,because of the simple design. In addition, this structure is adapted tousing heavier metals such as gold or silver for making overtone devices,allowing more flexibility in manufacturing as well.

In a preferred embodiment, the mass loading structures 34 include asubstantially repeating pattern on both surfaces 14 and 16 for minimaldifferences in mass loading between the electroded and unelectrodedregions 44 and 46.

Shown in FIGS. 5 and 6, is another piezoelectric resonator 100 withgrid-like electrodes. The piezoelectric resonator 100, includes apiezoelectric crystal plate 102 having opposite surfaces comprising topand bottom surfaces 104 and 106 and a plurality of electrodes includinga top and bottom electrode 108 and 114. The top electrode 108 includesleft and right sections 110 and 112 and the bottom electrode 114includes a left and right section 116 and 118. The electrodes aresuitably energized through tabs 120 and 122 which include narrow necksections and rectangular bases, in one embodiment. The plurality ofelectrodes 108 and 114 are in substantially overlying relationship (indashed lines in FIGS. 5 and 6) on each of the opposite surfaces 104 and106, and provide a primary frequency mode of operation and spuriousmodes upon suitable energization. The electrodes 108 and 114 comprise agrid-like structure sufficiently constructed to provide a substantiallyuniform distribution of electrical charges over a desired area, definedas an electroded region 126. This structure helps to minimize unwantedspurs in fundamental and overtone responses. Another advantage is thatthis structure allows heavier metals, such as gold or silver, to be usedas the electrode, for more flexibility in manufacturing. Further, thisstructure provides a minimal difference in mass loading between theelectroded region 126 and the non-electroded region 128, for improvedattenuation of spurious responses.

The area between the electrodes 108 and 114 on the opposing surfaces 104and 106, can be defined as the electroded region 126 (shown in dashedlines in FIGS. 5 and 6). The area surrounding the electrodes is definedas the non-electroded region 128. The difference in mass per unit areabetween the electroded region 126 and the non-electroded region 128 isminimal, because of the lightweight construction of the grid-likestructure 124. This structure contributes to attenuating spurious(unwanted) responses.

The grid-like structure 124 has openings or spacings 130 which compriseonly the piezoelectric crystal plate 102. The grid-like structure 124includes strips such as longitudinal and lateral strips 132 and 134. Theopening 130 define spacings between the strips 132 and 134 which areabout the same as the thickness of the piezoelectric crystal plate 102or less.

The bulk wave piezoelectric device is driven by means of electric fieldthat is created between the device electrodes. The changing electricfield is converted into mechanical motion by means of the piezoelectriceffect. The spacing between the metal strips of the grid electrodeshould be kept sufficiently small so that the electric field between theelectrodes is not adversely affected, as compared to a solid electrode.This will contribute to assuring that the motional parameters of thedevice are not significantly negatively influenced.

The grid-like structure 124 further includes strip widths 136 which areabout the same size as the openings (or spacings) 130 or less.

If the width of the openings were much smaller than the width of thestrips, the electrode mass would still be reduced but by aninsignificant amount. In a preferred embodiment, the mass of theelectrode is reduced by 25% or more as compared to a solid electrodewith similar dimensions, which requires that the openings collectivelyallow for reduction of the metal surface by 25% or more. This can beachieved when the opening sizes are comparable to the width of the metalstrips, assuming that the openings are of a substantially square shape.

The strip width 136 is sufficiently wide to provide a predeterminedelectrical conductivity. For example, if they are excessively narrow,the strips could have an undesirably high resistance and if they weretoo thick, the lightweight construction of the electrodes may not beachieved, further requiring tiles in the non-electroded region 128, forexample.

The strips 132 and 134 in FIGS. 5 and 6 are shown in a longitudinal andlateral direction, and could have other various modifications andpermutations. In any event, all of the strips 132 and 134 at least inthe electroded region 126 are electrically connected, in such a mannerso as to provide a substantially uniform distribution of electricalcharges over the electroded region 126, for improved attenuation ofspurious responses.

The strips 132 and 134 can comprise a heavy metal, and in some cases, alight metal may be desirable as well. Using a heavy metal such as goldor silver, can be advantageous from the standpoint that it can providegreater flexibility in manufacturing under many circumstances.

The longitudinal and lateral strips 132 and 134 are connected atintersection areas 138. The strips in intersection areas 138 havegenerally the same thickness as the strips 132 and 134 themselves, forsimplified manufacturing.

The grid-like structure 124 includes a mass per unit area of less thanor equal to about 75% of the mass per unit area of a solid electrodewith similar dimensions, for improved attenuation of spurious responses.

The grid-like structure 124 (electrodes 108 and 114) include ametallized layer on the top and bottom surfaces 104 and 106 which aresufficiently thick to provide the desired conductivity.

The grid-like structure 124 includes a substantially uniform pattern atleast throughout the electroded region 126 to provide a substantiallyuniform distribution of electrical charges over the electroded region126.

As used herein, the term "grid-like structure" can be defined as agrating, or a meshed or network of conductive lines (or strips) forproviding a substantially uniform distribution of electrical chargesover an electroded region. As should be understood by those skilled inthe art, various modifications and substitutions of the pattern, holes,strips, etc. can be made. The grid-like structure can also be thought ofas having openings between the strips defining a network having apredetermined number of openings per linear inch, which in a preferredembodiment are evenly distributed and spaced, comprising an interlockingand conductive and lightweight grid-like network structure, forproviding a substantially uniform distribution of electrical chargesover the electroded region.

The resonator 10 can be made in the following manner. The resonator canbe made with a photolithographic process. The process starts withgenerally a 2" square wafer. The wafer is etched in an acid until itbecomes the desired thickness. This thickness will determine theoperating frequency of the final crystal.

Next, a metal layer whose thickness can vary from 300 to 5,000angstroms, is placed over the etched wafer. Preferably, silver or goldis used as the metal. This metal layer covers both sides of the wafer,and can be used to make the electrodes on each individual crystal.

Once the metal conductive layer is placed on the wafer, a layer ofphotoresist is placed on both sides of the wafer on the metal layer. Thephotoresist breaks down in the presence of ultra-violet light. This canprovide a very accurate pattern to be placed on the photoquartz wafer.

The next step involves masking both surfaces of the wafer and exposingthe wafer to ultra-violet light. This enables the wafer to be divided upinto about 140 individual crystal filters.

A second mask can then be placed on the wafers. The second mask definesthe electrode pattern (grid-like structure), on the plurality ofindividual crystals.

After these two masks have been exposed, the conductive material can beremoved (where the photoresist was exposed to ultra-violet light). Thiswill enable the conductive material to be etched away and the 140 or socrystals to be etched out of the wafer.

The remaining photoresist is stripped off the wafer and what remains isa 2" square wafer with about 140 individual crystal resonators on it.

COMPARATIVE EXAMPLE A

The crystal filter as shown in FIG. 2 was built with solid electrodes,and without the tiles (mass loading structures 34) in ComparativeExample A. The dimensions of the filter were 0.18" by 0.10". The devicewas a third overtone quartz crystal filter having a center frequency ofabout 46 MHz and a bandwidth of 20 kHz. The electrodes were made out ofgold and had a thickness of 2000 angstrom. This conventional resonatorexhibited a frequency response 60 as shown in FIG. 3. Disadvantageously,a number of unwanted spurious responses were exhibited. The spurresonances in response 60 are very significant with the strongestresonance being 6 dB below the filter passband.

EXAMPLE 1

A second filter was built as shown in FIG. 2, and the tile similar tothat described with respect to Comparative Example A, however Example 1included the tiles (or mass loading structures) covering most of theunelectroded area of the quartz substrate. The electrodes and tiles weremade of gold having thickness of 2000 angstrom. The tile structures wereof a square shape with a side dimension of 0.003". The spacing betweenthe tile structures was 0.001". The frequency response corresponding toExample 1, is shown in FIG. 4 as item 62. Advantageously, the frequencyresponse 62 in FIG. 4, shows reduced spur responses, with the strongestspur being about 18 dB below the filter passband. The other electricalcharacteristics, in particular corresponding to the filter passband,were similar to that described with respect to Comparative Example A.Example 1 exhibited a substantial improvement in the reduction of spursas compared to Comparative Example A. This design can be easilyreplicated in large volumes, without major processing alternations oradditional expenses capital outlays for equipment and the like.

EXAMPLE 2

A second filter was built as shown in FIGS. 5 and 6. The filter inExample 2 is similar to that described with respect to ComparativeExample A. The overall dimensions were substantially the same. However,the grid-like electrodes were incorporated in Example 2, as shown anddescribed herein. The electrode material was gold having a thickness of2000 angstrom. The width of the vertical and horizontal strips wasdesigned to be 0.001". The openings were of a square shape with a sidedimension of 0.003". The frequency response corresponding to Example 2,is shown in FIG. 7 as item 64. Advantageously, the frequency response 64in FIG. 7 shows reduced spur responses, with the strongest spur beingabout 16 dB below the filter passband. Example 2 exhibited a substantialimprovement in the reduction of spurs as compared to Comparative ExampleA (a solid electrode pattern). The mass per unit area of thegrid-structure was about 43% of the mass per unit area of the solidelectrode pattern of Comparative Example A. This design can be easilyreplicated in large volumes, without major processing alterations oradditional expenses and capital outlays for equipment and the like.

Although the present invention has been described with reference tocertain preferred embodiments, numerous modifications and variations canbe made by those skilled in the art without departing from the novelspirit and scope of this invention.

What is claimed is:
 1. A piezoelectric resonator with an attenuatedspurious frequency response, comprising:a piezoelectric crystal platehaving opposite surfaces; a plurality of electrodes in substantiallyoverlying relationship deposited on each of the opposite surfacesdefining an electroded area, and providing a primary frequency mode ofoperation and spurious frequency modes upon suitable energization; atleast one of the electrodes comprise a grid-like structure deposited onat least one of the surfaces constructed to provide a substantiallyuniform distribution of electrical charges over the area of theelectrodes, whereby the uniform distribution helps minimize unwantedspurious frequency modes; and the electroded area having a substantiallysimilar mass per unit area as a surrounding unelectroded area such thata difference in natural resonant frequencies between the electroded andthe unelectroded areas is minimized.
 2. The piezoelectric resonator ofclaim 1, wherein the grid-like structure has openings and includesstrips, the openings defining spacings which are about the same distanceas a thickness of the crystal plate, or less.
 3. The piezoelectricresonator of claim 1, wherein the grid-like structure with openings,includes strips having a width about the same size as the openings, orless.
 4. The piezoelectric resonator of claim 1, wherein the grid-likestructure includes strips sufficiently wide to provide a predeterminedelectrical conductivity.
 5. The piezoelectric resonator of claim 1,wherein the grid-like structure includes strips which are electricallyconnected.
 6. The piezoelectric resonator of claim 1, wherein thegrid-like structure includes strips comprising a heavy metal.
 7. Thepiezoelectric resonator of claim 1, wherein the grid-like structurecomprises a mass per unit area of less than or equal to about 75% of themass per unit area of a solid electrode.
 8. The piezoelectric resonatorof claim 1, wherein the grid-like structure includes strips which aresufficiently thick to provide a predetermined conductivity.
 9. Thepiezoelectric resonator of claim 1, wherein the grid-like structureincludes a substantially uniform pattern in an electroded region.
 10. Apiezoelectric resonator with an attenuated spurious frequency response,comprising:a piezoelectric crystal plate having opposite surfaces; aplurality of electrodes in substantially overlying relationshipdeposited on each of the opposite surfaces defining an electroded area,and providing a primary frequency mode of operation and spuriousfrequency modes upon suitable energization; at least one of theelectrodes comprise an electrically connected grid-like structuredeposited on at least one of the surfaces constructed to minimize totalelectrode weight and provide a substantially uniform distribution ofelectrical charges over the electroded area, whereby the uniformdistribution minimizes unwanted spurious frequency modes; the grid-likestructure includes substantially uniformly patterned intersecting stripswhich provide a predetermined electrical conductivity having spacingsbetween the strips which are about the same as a thickness of thecrystal plate; and the electroded area having a substantially similarmass per unit area as a surrounding unelectroded area such that adifference in natural resonant frequencies between the electroded andunelectroded areas is minimized.